Scanner characterization for printer calibration

ABSTRACT

Colors similar to those which would be used in calibrating a target printer are printed on a printer of the same model and with the same materials set as anticipated for the printer calibration. These all lie within a substantially reduced portion of the gamuts of both the printer and scanner. A scanner characterization is derived only for those portions of color space corresponding to the printed colors. This may be done using spline fitting in one or more dimensions. While generic scanner calibrations generally have errors in excess of ΔE=7, with these techniques values generally less than 1.7 were obtained. This is sufficient for printer calibration.

CROSS REFERENCE TO RELATED PATENTS AND APPLICATIONS

This application is related to U.S. application Ser. No. 11/170,873,filed on Jun. 30, 2005, entitled COLOR CHARACTERIZATION OR CALIBRATIONTARGETS WITH NOISE-DEPENDENT PATCH SIZE OR NUMBER, by R. Victor Klassenand U.S. application Ser. No. 11/170,975, filed on Jun. 30, 2005,entitled METHOD AND SYSTEM FOR PROCESSING SCANNED PATCHES FOR USE INIMAGING DEVICE CALIBRATION, by R. Victor Klassen, and, U.S. applicationSer. No. 11/268,294 (Attorney Docket No. XERZ 2 00997), filed on Nov. 4,2005, entitled A METHOD FOR CORRECTING INTEGRATING CAVITY EFFECT FORCALIBRATION AND/OR CHARACTERIZATION TARGETS by R. Victor Klassen, all ofwhich are incorporated herein by reference in their entirety.

This application is based on and claims priority to U.S. ProvisionalApplication Ser. No. 60/733,467, filed Nov. 4, 2005, which applicationis hereby incorporated herein by reference in its entirety.

BACKGROUND

Scanner characterization traditionally suffers from a compromise betweenvery data intensive fitting or simplified model based characterizationwith less accuracy than is desired for using the scanner for subsequentprinter calibration. The emphasis on scanner calibration in the past wascalibration for unknown inputs—either unknown grey component replacementstrategy or unknown input media. This meant that the calibration was anattempt to do well in a larger domain of inputs, rather than doing verywell in a restricted domain.

To characterize a scanner for printer calibration, typically a number ofpatches of various colors are printed, measured with a known instrument(such as a spectrophotometer), scanned and patch averages are computed.

The usual goal of scanner characterization is to obtain the bestpossible result when scanning pages of unknown origin. Such pages may ormay not be halftones, and they typically contain image content, ratherthan simple collections of constant patches. Lack of informationregarding paper color (and fluorescence) and colorant materials limitsthe quality of such characterizations.

Sharma et al., G. Sharma, S. Wang, D. Sidavanahalli and K. Knox “Theimpact of UCR on scanner calibration”, in Proc PICS Conf., pp. 121-124,Portland, Oreg. (1998) describe the impact an unknown amount of blacksubstitution can have on scanner characterization. In the worst case,they found errors as high as 4.5 (mean ΔE), while when it was fullyknown, mean errors dropped below 1.2. When calibrating printers, thereis generally no black substitution. It suffices to characterize thescanner for this case.

Many others have characterized scanners. Ostromoukhov et al., V.Ostromoukhov, R. D. Hersch, C. Péraire, P. Emmel, I. Amidror, “Twoapproaches in scanner-printer calibration: calorimetric space-based vs.closed-loop”, in Proc SPIE 2170, pp. 133-142(1994) obtained results of2.37 (mean ΔE ). One reason for their poorer results is that the printerwas a desktop inkjet printer, with more noise and lower stability thanthe Xerographic printer used by Sharma et al. They noted neighborhoodeffects, and attempted to reduce their impact by using large patches.This may give incorrect results. Hardeberg, J. Hardeberg, “DesktopScanning to sRGB” in IS&T and SPIE's Device Independent Color, ColorHardcopy and Graphic Arts V, San Jose, Calif. (January 2000), optimizeda third order (3×20) matrix, obtaining ΔE 1.4 on two scanners, with lessgood results on others. Previously, Haneishi et al., H. Haneishi, T.Hirao, A. Shimazu, and Y. Miyake, “Colorimetric precision in scannercalibration using matrices”, in Proceedings of IS&T and SID'S 3^(rd)Color Imaging Conference: Color Science, Systems and Applications, pp.106-108, Scottsdale, Ariz. (November 1995), had obtained ΔE=2 using asecond (3×10) matrix regression. Rao, A. R. Rao, “Color calibration of acolorimetric scanner using non-linear least squares”, in Proc. IS&T's1998 PICS Conference, Portland, Oreg. (May 1998), obtained similarvalues. Hardeberg's thesis, J. Hardeberg, Acquisition and Reproductionof Colour Images: Colorimetric and Multispectral Approaches, DoctoralDissertation, l'Ecole Nationale Supérieure des Télécommunications (Paris1999), describes an experiment (p. 37ff.) in which a single scanner ischaracterized with a mean ΔE of 0.92, a max of 4.67 and a 95^(th)percentile of 2.25 on a set of 288 patches (the same set used tocalibrate). He also characterized and tested on (disjoint) subsets (p.51), and found that when he used 144 patches to train, and the other 144to test, the mean ΔE rose to 0.96, but the max (of the test set) fell to3.36 (the max ΔE for the training set was higher, at 3.9).

Because scanners are not colorimetric, they may exhibit metamerism:colors that appear identical to a scanner might appear different to ahuman observer. For fixed media and black substitution strategymetamerism is not a problem. However, the conversion from RGB to XYZvarious throughout color space. As compensation, scanners may measurefar more patches per minute than spectrophotometers inasmuch as we canafford to sample color space substantially more densely.

The only difference between characterizing a scanner for printercalibration and characterizing it for arbitrary prints from that printeris the sampling of color space. While there is no need to characterizethe scanner in regions of color space which are not used for printercalibration, all regions are typically sampled in the more general case.

By way of background, methods of printer calibration are described, withparticular reference to the portions of color space they each seek tocontrol.

One type of printer calibration involves ΔE from paper. For this printercalibration, a step wedge in each separation is used. In betterimplementations, the step wedge is linear in ΔE distance from paper, aspredicted by the previous calibration. As a result, we cannot predictexactly which color will be needed but we can say they will be along theCMYK axes. These axes do not (exactly) run along lines in L*a*b* space,but they are confined to space curves, which stay relatively fixed. Thatis, it is sufficient to be able to estimate the location along thecurve, and ignore any deviation from the curve. What matters is theability of the measuring device (in this case a scanner) to detect smallchanges along that line.

Another type of printer calibration uses Grey Balance Tone ReproductionCurves (TRC). For this calibration, patches surrounding the presumedneutral axis are printed and measured, in order to find a betterapproximation of the location of the neutral axis. The neutral axis isthen divided into equal increments along L* and CMY points along thataxis define the TRCs. The neutral axis does not generally go to the fullCMY point, as one of the three defines the limit of the CMY neutral. Theothers are then smoothly carried out to their limits. The procedurenormally begins with a good estimate of the printer response, from acombination of a full characterization and any previous grey balancecalibrations. The refinement is only CMY patches close to the neutralaxis. A separate ΔE from paper TRC is built for the black separation.

In terms of being able to do a grey balance TRC with a scanner, theissue is how well can the scanner be calibrated near the neutral axis,and, once calibrated, how sensitive is it to small changes in bothlightness along the axis and changes perpendicular to the axis.

Another type of printer calibration uses a two-dimensional tonereproduction curve (TRC). In this version, there are three twodimensional tables built, for CMY space. One maps from (C, M+Y) to C′,another from (M, C+Y) to M′, and the third from (Y, C+M) to Y′.Considering only the first one, the table is built with ΔE from paperalong the M+Y=0 axis, grey balance along the line C=(M+Y)/2, ΔE from redalong the line from white to red, ΔE from red along the line from red toblack, and ΔE from cyan along the line from cyan to black. One otherline is typically controlled, using a compromise between ΔE from paperto blue and to green along the line from (0,0) to (0,1). Similar linesare controlled for the other two tables. This means that the followinglines through color space are controlled: paper to C, M, Y, R, G, B;paper to CMY; CMY to C, M, Y, R, G and B; paper to K. Many of these arelines that were controlled in one of the prior two calibrations. The newlines are all controlled in a one-dimensional sense, just as for the ΔEfrom paper calibration, so again, the only thing that substantiallymatters for them is the scanner response to small changes along a curve,and not orthogonal to the curve.

Still another type of printer calibration involves a three-dimensionaltone reproduction curve (TRC). In this version, all of color space issampled, but coarsely. That is, a relatively coarse grid in CMY space isused to obtain a 3D correction function. If, e.g. a 7×7×7 grid of CMYpoints is used to calibrate the printer, it is colors in theneighborhood of those 343 patches that matter.

BRIEF DESCRIPTION

In accord with the presently described embodiments, in one form, colorssimilar to those which would be used in calibrating a target printer areprinted on a printer of the same model and with the same materials setas anticipated for the printer calibration. These all lie within asubstantially reduced portion of the gamuts of both the printer andscanner. A scanner characterization is derived only for those portionsof color space corresponding to the printed colors. This may be doneusing spline fitting in one or more dimensions. While generic scannercalibrations generally have errors in excess of ΔE=7, with thesetechniques values generally less than 1.7 were obtained. This issufficient for printer calibration.

In this regard, in one aspect of the presently described embodiments,the method comprises determining regions of a color space to be printedby the printer, printing color patches, by the printer, corresponding tothe determined regions of the color space, scanning the color patcheswith the scanner, measuring device—independent color values for eachpatch calculating reflectance values for each patch, and, computing ascanner characterization function based on the reflectance values.

In another aspect of the presently described embodiments, the measuringcomprises using a spectrophotometer.

In another aspect of the presently described, embodiments, thedetermining comprises selecting colors in a region of color spacerequired in a later printer calibration.

In another aspect of the presently described embodiments, the laterprinter calibration comprises ΔE from paper calibration.

In another aspect of the presently described embodiments, the laterprinter calibration comprises grey balance calibration.

In another aspect of the presently described embodiments, the laterprinter calibration comprises two-dimensional calibration.

In another aspect of the presently described embodiments, the laterprinter calibration comprises three-dimensional table look-upcalibration.

In another aspect of the presently described embodiments, the determinedregions are locations on a grid.

In another aspect of the presently described embodiments, thecharacterization function is comprised of multiple independentcharacterizations.

In another aspect of the presently described embodiments, thecharacterization function is selected from among the multipleindependent characterization functions based on the printed color to beconverted.

In another aspect of the presently described embodiments, means areprovided to implement the method.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a scanner to which the presently describedembodiments may be applied;

FIG. 2 is an illustration of a system to which the presently describedembodiments may be applied; and,

FIG. 3 is a flow chart according to the presently described embodiments.

DETAILED DESCRIPTION

As noted above, there are currently practiced at least four methods ofprinter calibration: ΔE from paper TRC, Grey-balance TRC, 2D TRC and 3DLUT+K TRC.

According to the presently described embodiments, a scanner's responseis characterized in only that portion of color space needed for suchprinter color calibration. By limiting the region for which thecharacterization is valid, higher precision is possible with areasonable number of measurements.

To illustrate, referring now to the drawings where the showings are forthe purpose of describing an embodiment of the invention and not forlimiting same, FIG. 1 represents one possible embodiment of a desktopscanner having an image acquisition device which may be used with thepresently described embodiments. Although the presently describedembodiments are described in conjunction with a desktop scanner, it maybe possible to adapt it for use with other image acquisition devices,and the presently described embodiments are not limited to theseembodiments. For example, it may be implemented with a scanner that isclosely associated with a printing system.

Referring to FIG. 1, a desktop scanner 10 incorporates a transparentplaten 20 on which a document 22 to be scanned is located. One or morephotosensitive linear arrays 24 are supported for reciprocating scanningmovement below platen 20. A scanning system assembly includes severaloptical components which move together as a single unit. These typicallyinclude a fluorescent lamp 34, an associated reflector 26 and a baffle36, with the latter two elements cooperating to direct a narrow band oflight onto a small area across the platen. Also included in the assemblyare lens 28, and mirrors 30, 38 and 40, which operate together to focusthe illuminated segment of platen 20 and the document being scannedthereon, onto array 24. Array 24 produces image signals or pixelsrepresentative of the image present on the surface of document 22. Thesepixels are output to a display or storage device. The entire scanningsystem assembly is enclosed by cavity 50. Also shown is a processingmodule 32 in communication with the array 24. The processing module 32may take a variety of suitable forms and may reside within the cavity 50or outside the cavity 50. Further, the processing module 32 may beincorporated within the scanner or may reside on a system controllingthe scanner.

Scanning array 24 may be a linear array of photosensitive sensors suchas CCD's or photodiodes which are controlled to sense light reflectedfrom a document during the illumination period. The photosensitivesensors develop a charge indicative of the amount of light detected, fortransmission to an image processor for use in assimilating anelectronically stored representation of image contained in document 22.Scanning array 24 extends in a direction transverse to that of themotion of the carriage. This enables the carriage to move along an axisknown to those skilled in the art as the “slow scan” axis, which beginsat one end of the image and extends in the process direction towards theopposite end. The direction across the page in which the array extendsis known as the fast scan axis.

Color imaging is typically performed using various combinations ofcolors, most often three colors red, green and blue. The color sensor 44includes one filter for each color that will be used by the device forgenerating images. Thus, once the light from lamp 34 passes through lens28, it will reach color sensor 44, where it will be filtered into theseparate color sources.

In order to use the scanner as a surrogate for a spectrophotometer it isnecessary to correct raw scanner response to scanner-weightedreflectance and average the pixels within a window. Any outliers mayalso be removed at this stage. A process for doing so is described inU.S. patent application Ser. No. 11/170,975, entitled “METHOD AND SYSTEMFOR PROCESSING SCANNED PATCHES FOR USE IN IMAGING DEVICE CALIBRATION”,filed Jun. 30, 2005, the disclosure of which is incorporated herein byreference in its entirety. Given a method of converting from a scannedpatch on a page to a mean reflectance in each of red, green and blue (orpossibly more channels), an objective is to select patches to print, anduse their mean reflectances to compute a scanner characterizationfunction.

Scanner-weighted reflectance is the closest surrogate to reflectance onecan measure with a given scanner. While true reflectance is a functionof wavelength, scanner-weighted reflectance is the result of takingweighted averages of the spectral reflectances, where the weights areimplicitly defined by the filters used in separating the (typically red,green and blue) channels of the scanner. For simplicity, the term“reflectance” will be used for “scanner-weighted reflectance” with theunderstanding that it refers to a corrected response from one of thescanner's channels, and not an actual spectral reflectance. It isexpected that the reflectance, as corrected, is equal to the actualreflectance as reported by a spectrophotometer, when a neutral grey offlat spectral response is measured or scanned.

To illustrate, in an example implementation of the presently describedembodiments, with reference to FIG. 2, a system 100 is shown. The system100 includes the scanner 10, as more particularly described inconnection with FIG. 1. The system 100 also includes a printer 102. Theprinter 102 may take a variety of forms that are well known. Printer102, in one form, includes a print engine and associated components thatutilize color spaces which can be analyzed in accord with the objectivesof the presently described embodiments. In this regard, the scanner 10is characterized based on the color space used by the printer 102. Itshould also be noted that the printer 102 will typically handle an imageinput 104 which will be suitably processed by the printer 102 to obtaina printed output 106. The output 106, in one form, is then used by thescanner for characterization purposes in accord with the techniques ofthe presently described embodiments.

With reference now to FIG. 3, a method 200 according to the presentlydescribed embodiments is illustrated. It should be appreciated thatmethods, including method 200, according to the presently describedembodiments may be implemented in a variety of manners. For example, avariety of hardware configurations and software techniques may beimplemented to realize the objectives of the presently describedembodiments. For example, printing functions (e.g., at 202, 204) of themethod may be carried out by the printer 102 while scanning and otherprocessing functions (e.g., 206, 208, 210) of the method will be carriedout by the scanner 10 and its associated processing module 32. In thisregard, suitable software routines may be housed and processed by module32. In some forms, a spectrophotometer may be used to measure selectedvalues, as illustrated below.

With reference back to FIG. 3, the method 200 includes determining theregions of color space to be printed (at 202). This determination, in atleast one form, comprises selecting colors in a region of color spacerequired in a later printer calibration, e.g., grey balance calibration,ΔE from paper calibration, two-dimensional calibration and/orthree-dimensional table look-up calibration. Color patches correspondingto the determined regions of color space are then printed (at 204). Thisprinted output (i.e., 106 of FIG. 2) is then scanned and measured (at206). In one form, the scanning is carried out by the scanner 10 (ofFIG. 2). Device-independent color values for each patch are thenmeasured. A spectrophotometer may be used to do so. Reflectance values(e.g., L*a*b* values) for the patches are then calculated for each colorchannel (at 208). A scanner characterization function is then computedbased on the reflectance values and the device-independent color values(at 210). The characterization functions may be comprised of multipleindependent characterization functions. Further, the characterizationfunction may be selected from the multiple independent characterizationfunctions based on the printed color to be converted.

It should be understood that the calculation of reflectance values(e.g., at 208) for each color channel and the computation of scannercharacterization (e.g., at 210) may be accomplished according to thepresently described embodiments in a variety of manners. For example,the manner selected to accomplish these objectives may depend on theprinter calibration methods that may ultimately be used for purposes ofcalibrating the printer 102.

So, in one embodiment, ΔE from paper is considered. In this case, thereare four step wedges: one per printed separation. These may be printedat sufficient (e.g. 33 levels) resolution, scanned and converted toreflectance values. For each scanner channel (normally R,G,B), a spacecurve is fit mapping averaged R, G or B to measured L*, a* and b*. Thisprovides three different parameterizations of what is the same spacecurve. One such space curve is found for each separation independentlycontrolled (e.g. cyan, magenta, yellow and black).

To find L*a*b* values for a given input RGB, the closest point on thespace curve corresponding to the appropriate printed color is found.Unless the point is actually on the curve (unlikely given measurementimprecision), the L*a*b* values given by the three curve representationswill differ, since small errors in each of R, G, and B will each lead todifferent locations on the curve. As a result, a search mechanism isemployed that minimizes the difference between the location in L*a*b*space and the three locations predicted by the R, G and B values, whilestaying on the curve. From the computed L*a*b* value, ΔE may becomputed.

A B-spline curve with optimized knot locations has been found to workwell for representing the space curve. If an approximate calibration ofthe printer exists, in terms of scanner RGB, the printed values can bechosen so as to provide an approximately even sampling of scanner RGBspace along the curve going from white to full toner. Having theparameter space evenly sampled tends to improve the quality of the fit.

At this point there are three representations of the same curve throughL*a*b* space, each with a different input parameter. Each point on thecurve is a three dimensional point in L*a*b* space. The three curvestogether represent a mapping from (RGB) to (L*a*b*), but only for asingle set of (RGB) points. For a given RGB triplet, there is the chancethat the L*a*b* values corresponding to R will be the same as thosecorresponding to G, and to B. As long as only a single separation ismeasured to generate that RGB triplet and that is the same separationthat was used to create the space curves, it is likely that the L*a*b*values corresponding to the three inputs will be close, but it isunlikely, given measurement noise, that they will be identical.

Therefore, to find L*a*b* values for a given input RGB, the closestpoint on the three space curves is found. That is, the three L*a*b*points on the respective R, G and B curves are found. For each of thosethree points, there exists an input parameter corresponding to thefraction of the way along the initial step wedge that that point is.These will in general be close to each other, but different. Anoptimization procedure attempts to find the parameter value where thedifference between the RGB for that parameter value and the R, G, and Bvalues measured is minimized, in a least squares sense. That is, each ofthe three points R, G and B corresponds to a parameter pr, pg, pb. Eachof these parameters has associated with it an amount of all threeseparations, R, G and B. Some value of the parameter minimizes thesquared sum of differences between its corresponding R, G and B and theRGB value read by the scanner. It is this value of the parameter that isthen evaluated in computing the L*a*b* values of the measured patch,from which the ΔE from paper value is calculated.

In another embodiment, grey balance TRCs are used. Here the problem isthree dimensional. Not only is it important to have uniform steps inlightness, it is possibly more important to confine those steps to theneutral axis.

Ideally, one would define a line from white to black, and print, measureand model a square prism through color space along that line. That is,for each of some number of points along the line, print a 5×5 grid ofpoints at locations regularly spaced on a plane perpendicular to theline. This works for much of color space, but not for colors close toblack or white. Suppose, one defines a (g,r,y) space, (for grey, red,yellow: note the use of lower case, as upper case R and G are already inuse for Red and Green), based on the transformation of the CMYcoordinates:g=(C+M+Y)/3r=(M+Y−2C)/2y=(2Y−M−C)/2

Then, taking equal steps up the g axis takes one from white to black,along printer neutral. For any given value of g, two equal steps in eachdirection (positive and negative) away from the axis in each of r and ydefines a 5×5 grid. Steps of 1/16 of the printer gamut appear sufficientto ensure that the actual neutral axis is contained within the modeledregion. Unfortunately, some of these points are out of gamut. Forexample (0.0625, 0.125, 0.0) corresponds to C+M+Y=0.1875, M+Y−2C=0.25and Y=(M+C)/2. Substituting the last into the other two:

M+C=0.125 and 3(M−C)=0.5; C=− 1/48, which is physically impossible.Hence, only the realizable subset of this group of patches can beprinted and measured.

The remaining ones may be extrapolated. Since it is not anticipated thatcolors far from the neutral axis will be printed and scanned, errorscaused by extrapolation should have little effect on the result.

Once all of the patches are printed and measured, they may be defined interms of 25 columns of values, parameterized by their g value. Eachcolumn may be fit to a single B spline curve (or another parametricform), and then from the parametric fit an extrapolation may be obtainedto fill in the remaining points outside of the gamut. At any givenlevel, the 25 splines may be evaluated to give a set of estimates ofsmoothed values at that level. From those smoothed values, a tensorproduct (single segment) B spline may be formed, allowing a smoothinterpolation anywhere within the level. By evaluating the interpolatingfunction within each level, new columns may be computed, which smoothlyinterpolate between the existing ones. Now there are two threedimensional functions of the parameters g,ry: one giving RGB as afunction of gry, and another giving L*a*b* as a function of gry.

Defining yet another set of coordinates similar to gry, called g′r′y′,in terms of RGB, based on the transformation R=1−C, G=1−M, B=1−Y, onemay then form a regular, moderately finely sampled grid in g′r′y′ space.A point in this new grid is populated by:

converting from its g′r′y′ coordinates to RGB;

finding that RGB in the mapping from gry to RGB;

using the gry where the RGB was found; and

computing the corresponding L*a*b* by interpolation.

Once all of the patches are printed and measured, they may be fit to asingle 3D B spline (or an other parametric form). This function gives adirect mapping from scanner GRY (the input parameter space) to printerL*a*b*. Using an input parameter space that aligns with the major axisof the data sample points leads to a much better fit, than say,attempting to do a fit from RGB to L*a*b*, when the input data iscentered along the neutral axis.

Several manipulations are helpful in improving the fit:

1) Space the input (printed) data (approximately) uniformly throughscanner GRY space. (This is naturally imperfect, as it requires ascanner characterization, which we are building).

2) Use Singular value decomposition to find the BSpline control vertexvalues.

3) Transform the scanned values into a more uniform, axis-aligned spacebefore using them as parameters to fit the L*a*b* spline. That is,rotate their principal component axis to align with the g axis, andscale all three axes to fill space more uniformly.

4) Integrating cavity effect correction, as described in U.S.application Ser. No. 11/268,294 (Attorney Docket No. XERZ 2 00997),filed on Nov. 4, 2005, entitled A METHOD FOR CORRECTING INTEGRATINGCAVITY EFFECT FOR CALIBRATION AND/OR CHARACTERIZATION TARGETS by R.Victor Klassen, the disclosure of which is incorporated herein byreference in its entirety, is recommended, prior to any data fitting.

5) Maximize the number of patches on the printed page: with 29 planes ofpatches rather than 24, a 30% improvement in the quality of fit wasobtained.

In another embodiment, two-dimensional TRCs are used. The data for 2Dmethods is the same as the data for the two above methods combined,along with additional lines that are all controlled in a one-dimensionalsense, analogous to ΔE from paper. Thus, the approach to characterizingthe scanner for ΔE from paper applies to the new regions, while one ofthe above approaches applies to all the other regions. The overallcharacterization function combines the characterization functions of allthe individual TRCs. When a given color is to be converted from scanvalues to device independent values, it is known to which region of(printer) color space that color belongs. A separate characterizationfunction may be used for each such region, and selected based on theprinted color to be converted.

While full characterization typically yields values of ΔE in excess of7, this method has produced values less than 0.9, at the 95^(th)percentile. The maximum error was 1.8, and the mean was 0.3. The qualitywas measured by comparing the L*a*b* values of the input points, asmeasured using a spectrophotometer, to the L*a*b* values predicted, inthe neutral axis fitting (single separation values tend to be somewhatbetter).

Hue Control Along Multiple-Separation Axes

When characterizing the scanner for printer calibration, measurementalong the following lines may be had:

1) White to primaries

a. White to magenta

b. White to yellow

d. (White to black)

2) White to Secondaries

a. White to red

b. White to green

c. White to blue

3) White to black along the neutral axis, in a thick swath.

4) Black to primaries

a. Black to cyan

b. Black to magenta

c. Black to yellow

5) Black to secondaries

a. Black to red

b. Black to green

c. Black to blue

The first group is then used for a ΔE from paper TRC for each of therespective primary colors. There is the implicit assumption that thelocus of colors along which a tint of any primary can lie is fixed, andso any newly measured color made from such a tint will be within noiseof this locus, and it is only along that locus that we measure and fit acurve to characterize the scanner.

The third group we attempt to sample broadly and densely enough thatthere is no issue of colors near C=M=Y will produce a color outside thegamut for which the scanner was characterized, and the fit to thecharacterization data should then take care of any near neutral we mightmeasure.

The remaining groups are subject to variations in the printer,specifically in the ratio of separations that appear when more than oneis requested, even though they are requested in equal amounts.

White to Secondaries

Taking the example of white to red, the primary source of variation isin the ratio of magenta to yellow along this line. Colors will generallystay very close to the “plane” defined by red, magenta, yellow andwhite, but may not stay along the line originally measured using equalamounts of requested magenta and yellow. There may be three onedimensional B splines running from white to red, (one each for L*, a*and b*). These are from white to printer red, not necessarily scannerred. Stepping (say) 1/16 of the printer gamut toward magenta, we canmeasure along a second line, from Y=O, M= 1/16 through Y= 15/16, M=1.This line could be sampled at half the density of the original line fromwhite to red. A second one dimensional set of B-splines can then be fitthrough these points. Similarly, we can measure a third line from M=O,Y= 1/16 through M= 15/16, Y=1, and fit a set of splines through it. Now,given these three splines, we can step at fairly frequent steps from oneend to the other (e.g., like 128), and build a two-dimensionaltriangular mesh connecting fitted points in the three lines together. Itshould be safe to linearly extrapolate beyond the triangular mesh to theedges of the scanner gamut. Then, we can sample the scanner's spacedensely and build a rectangular mesh that is uniform in scanner RGBspace, for fast searching.

This adds two new lines to measure (per separation), two new sets ofcurves to fit (each), and some post-processing to make it reasonablyfast to find an L*a*b* value from a scan of a printed color along one ofthese lines.

Black to Primaries

Taking cyan as a representative primary, this is a case where cyan isheld constant through the ramp and yellow and magenta are stepped from 0to 1 in unison. This is perfectly analogous to the white to secondariescase, and can be handled in like fashion. It should be safe to assumethat colors printed with full cyan will not wander much from the surfaceof the cube face, but may wander within the face as the ratio of yellowand magenta varies.

Black to Secondaries

Here a representative sample could be black to red. Cyan is varied alongthis line, while magenta and yellow are held fixed at their maxima. Tofirst order, we can assume that magenta and yellow produce a constantred, and that never changes. To the extent that is a valid assumption,we need make no further measurements to accommodate these colors.

The second order assumption is that red moves about some. In that case,we can print and measure three parallel lines (again at lower resolutionthan the original line along the gamut edge). One line would be at Y=15/16, M=1, another at Y=1, M= 15/16, and the third at Y=M= 15/16. Thiswould give us four fit curves along the edge of the gamut, and bysampling those fits we can put together a grid of points (2×2×n) alongthe edge. Here, n is the desired sampling resolution along the lines. Wecan further linearly extrapolate to 17/16 to expand the grid to 3×3×nwith the black to red line running up the middle of the grid. Then, whenwe measure a color purported to be along the black-red line, we caninterpolate within this grid.

Using this approach would require an additional three lines times threesecondaries, for nine more lines.

In still other embodiments, three-dimensional lookup tables are used.For three-dimensional lookup tables, patches at known locationsthroughout color space are printed in the calibration process. Thescanner characterization should aim to maximize accuracy in the vicinityof each of those locations. For example, if the patches are arrayed on auniform grid, the same grid could be used when the scanner ischaracterized. While the colors printed on a subsequent calibration willnot be a perfect match, the scanner characterization will be better inthose locations than (say) mid-way between the locations for which thescanner was characterized.

It will be appreciated that various of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. Also thatvarious presently unforeseen or unanticipated alternatives,modifications, variations or improvements therein may be subsequently.made by those skilled in the art which are also intended to beencompassed by the presently described embodiments.

1. A method for characterizing a scanner associated with a printer, themethod comprising: determining regions of a color space to be printed bythe printer; printing color patches, by the printer, corresponding tothe determined regions of the color space; scanning the color patcheswith the scanner; measuring device-independent color values for eachpatch; calculating reflectance values for each patch; and, computing ascanner characterization function based on the reflectance values andthe device-independent color values.
 2. The method as set forth in claim1 wherein the measuring comprises using a spectrophotometer.
 3. Themethod as set forth in claim 1 wherein the determining comprisesselecting colors in a region of color space required in a later printercalibration.
 4. The method as set forth in claim 3 wherein the laterprinter calibration comprises grey balance calibration.
 5. The method asset forth in claim 3 wherein the later printer calibration comprises ΔEfrom paper calibration.
 6. The method as set forth in claim 3 whereinthe later printer calibration comprises two dimensional calibration. 7.The method as set forth in claim 3 wherein the later printer calibrationcomprises three dimensional lookup table based calibration.
 8. Themethod as set forth in claim 7 wherein the determined regions arelocations arrayed on a grid.
 9. The method as set forth in claim 1wherein the characterization function is comprised of multipleindependent characterization functions.
 10. The method of claim 8wherein the characterization function is selected from among saidmultiple independent characterization functions based on the printedcolor to be converted.
 11. A system for characterizing a scannerassociated with a printer, the system comprising: means for determiningregions of a color space to be printed; means for printing colorpatches, corresponding to the determined regions of the color space;means for scanning the color patches; means for measuringdevice-independent color values for each patch; means for calculatingreflectance values for each patch; and, means for computing a scannercharacterization function based on the reflectance values and thedevice-independent color values.
 12. The system as set forth in claim 11wherein the means for measuring comprises using a spectrophotometer. 13.The system as set forth in claim 11 wherein the means for determiningcomprises selecting colors in a region of color space required in alater printer calibration.
 14. The system as set forth in claim 13wherein the later printer calibration comprises grey balancecalibration.
 15. The system as set forth in claim 13 wherein the laterprinter calibration comprises ΔE from paper calibration.
 16. The systemas set forth in claim 13 wherein the later printer calibration comprisestwo dimensional calibration.
 17. The system as set forth in claim 13wherein the later printer calibration comprises three dimensional lookuptable based calibration.
 18. The system as set forth in claim 17 whereinthe determined regions are locations arrayed on a grid.
 19. The systemas set forth in claim 11 wherein the characterization function iscomprised of multiple independent characterization functions.
 20. Thesystem of claim 19 wherein the characterization function is selectedfrom among said multiple independent characterization functions based onthe printed color to be converted.